math

Suppose 80% of citizens in Singapore are smokers. During a year, 50% of smokers suffer from at least one respiratory disease, but only 10% of non-smokers suffer from at least one respiratory disease. Suppose a citizen in Singapore is drawn randomly. Let S be the event that the selected citizen is a smoker. Let R be the event that the selected citizen is suffering from at least one respiratory disease. Given that a citizen has no respiratory disease in a year, what is the probability that s/he is a smoker?

Are events S and R independent if 30% of citizens in Singapore are smokers?

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